At the helm of the Gambia for 22 years, Jammeh's mandate expired at midnight (0000 GMT) with no sign of him stepping down.
The United Nations Security Council was to vote later Thursday on endorsing a west African military intervention as Senegal, Nigeria and Ghana dispatched hundreds of troops and fighter jets to The Gambia's border with Senegal.
Shops were shuttered and streets quiet in and around the capital Banjul with tour operators evacuating hundreds of tourists from the tiny country's popular beach resorts.
The army chief however has insisted his soldiers would not get involved in a "political dispute" nor prevent foreign forces from entering the west African nation.
Barrow, a real-estate agent turned politician who won a presidential vote on December 1, flew to Senegal on January 15 after weeks of rising tension over Jammeh's steady refusal to step down.
At the helm of the former British colony for 22 years, Jammeh's mandate expired at midnight (0000 GMT) with no sign of him stepping down.
He has attempted instead to block Barrow's inauguration with a court ruling and by declaring a state of emergency.
But Barrow's spokesman Halifa Sallah told AFP that the inauguration would go ahead. "It is going to take place at the Gambian embassy in Dakar ... at 4:00 pm (1600 GMT)," he said.
Jammeh initially acknowledged Barrow as the victor in December elections, but later rejected the result, this week declaring a national state of emergency.
Speaking to AFP by phone, senior coalition official Isatou Touray welcomed a declaration by army chief Ousman Badjie that his troops would not prevent Jammeh's removal by force.
"That's a very positive outlook from him, given that Jammeh's regime is done," Touray said.
"We don't have to risk the lives of innocent citizens."
In remarks at a hotel restaurant late Wednesday, Badjie said he loved his men and wouldn't risk their lives in a "stupid fight," eyewitnesses said.
- 'Really scary'
Arriving back at Manchester airport in northern England, several passengers could be seen comforting a Gambian national and UK resident who had tried unsuccessfully to get his family out.
Speaking to AFP, Ebrima Jajne described the situation as "really scary for everybody... because this president (Jammeh) doesn't want to step down and people are fleeing."
Tourist Ralph Newton said local residents had done what they could to reassure visitors, despite the threat to themselves.
"All the locals were just worried ... They said it's a bad time for us but you'll be all right... It'll be us they come for, if they come for anybody."
And Sara Wilkins, another tourist, said they had struggled to get clear information on the developing situation.
"We weren't told anything... I kept phoning Thomas Cook and they just like ... don't worry about it," she told AFP.
"I rang Thomas Cook again this morning and they said pack your bags, you've got to go."
Despite the build-up along the border, an army source told AFP Senegalese troops were "not yet" present on Gambian soil.
After 11th-hour talks in Banjul, Mauritanian President Mohamed Ould Abdel Aziz flew on to Dakar where he met Barrow for talks at which Senegal's President Macky Sall was also present, the private RFM radio station reported.
It was not clear whether the Mauritanian leader had secured a deal or made an asylum offer to Jammeh.
The last-minute intervention came after several unsuccessful attempts at diplomacy by the 15-nation Economic Community Of West African States (ECOWAS).
Mauritania is not part of ECOWAS and diplomats have previously reached out to the conservative desert nation in hopes of brokering a deal with Jammeh.
ECOWAS heads the regional force massing on Gambian-Senegalese border.
"ECOWAS has stood up, and they don't always do that", he said.
"It's an important message to Jammeh, both from the people of The Gambia, the people of Africa, and from neighbouring states, that it's not business as usual anymore."